We address the issue of maximizing the number of connected devices in a Narrowband Internet of Things (NB-IoT) network using non-orthogonal multiple access (NOMA) in the downlink. We first propose an optimal joint sub-carrier and power allocation strategy assuming perfect channel state information (CSI) called Stratified Device Allocation (SDA), that maximizes the connectivity under data rate, power and bandwidth constraints. Then, we generalize the connectivity maximization problem to the case of partial CSI, where only the distancedependent path-loss component of the channel gain is available at the base station (BS). We introduce a novel framework called the Stochastic Connectivity Optimization (SCO) framework. In this framework, we propose a heuristic improvement to SDA namely SDA with Excess Power (SDA-EP) algorithm for operation under partial CSI. Furthermore, we derive a concave approximation (SCO-CA) algorithm of near-optimal performance to SCO given the same amount of CSI. Through computer simulations, we show that SDA-EP and SCO-CA outperform conventional NOMA and OMA schemes in the presence of partial CSI over a wide range of service scenarios.